Question: Rewrite as a simplified fraction. ${3.15\overline{8} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3158.8888...\\ 100x &= 315.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 2843}$ ${x = \dfrac{2843}{900}} \text{or} {3 \dfrac{143}{900}}$